改进的一重积分不等式在时滞神经网络中的应用
The Application of Improved Single Integral Inequality in Neural Networks with Time-Delayed
摘要: 本文主要研究一类一重积分不等式的改进并将其用于分析时滞神经网络稳定性的问题。首先，借助交互凸组合不等式和多个零等式，改进一类一重积分不等式。其次，根据研究的时变时滞系统的属性，构造一类新的含有更多时滞信息的增广型Lyapunov泛函。然后，利用改进的积分不等式及其它分析技巧，获得保守性较低的稳定性判据。最后，通过一个数值例子验证所得结果的有效性和优越性。
Abstract: This paper is concerned with an improved single integral inequality with application in the time-delayed neural network. First of all, an improved single integral inequality is proposed by virtue of the reciprocally convex combination inequality and zero-qualities. Secondly, relay on the characteristics of the system more information about time-delay is considered in constructing the augmented Lyapunov functional. Then, a less conservative stability condition is obtained through utilizing the improved integral inequality and other analysis techniques. In the end, to verify the effectiveness and superiority of the derived results, a numerical example is provided.
文章引用：柳莹莹, 熊良林, 邹梅, 蔡丽, 王珍. 改进的一重积分不等式在时滞神经网络中的应用[J]. 理论数学, 2021, 11(1): 79-89. https://doi.org/10.12677/PM.2021.111012

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